A concave mirror forms a real image three times larger than the object on a screen. The object and screen are moved until the image becomes twice the size of the object. If the shift of the object is 6cm, find the shift of screen.

Explanation

`(v)/(u)=(I)/(o) =3` (i)
and `(v^('))/(u^('))=(I)/(o)=2rArr (v^('))/(u+6) =2` (ii)
Form (i) and (ii), we get
` v^(') =2((v)/(3)+6)` (iii)
`rArr v^(')-(2)/(3)v=12`
`(1)/(v)+(1)/(u)=(1)/(f)=(1)/(v^('))+(1)/(u^('))`
`rArr (1)/(v)+(3)/(u)=(1)/(v^('))+(2)/(u^('))`
`rArr 4((3)/(2)-1)`
`rArr v=(4)/(3)v^(')` (iv)
From (iii) and (iv),
`v^(')-(2)/(3)xx(4)/(3)upsilon^(')=12 `
`rArr (1)/(9)v^(')=12rArr v^(')=108 cm`
`rArr v=(4)/(3)v^(')=144cm`
Shifting will be `144-108=36 cm` toward the image.